Show the Proof

import proveit
# Automation is not needed when only showing a stored proof:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%show_proof

	step type	requirements	statement
0	instantiation	1, 2	,  ⊢
	:
1	axiom		⊢
	proveit.logic.booleans.eq_true_intro
2	instantiation	3, 4, 5	,  ⊢
	: , : , :
3	theorem		⊢
	proveit.logic.equality.sub_left_side_into
4	instantiation	6, 7, 66, 8, 9, 10*, 11*	,  ⊢
	: , : , :
5	instantiation	12, 13, 14*	,  ⊢
	:
6	theorem		⊢
	proveit.numbers.addition.strong_bound_via_left_term_bound
7	instantiation	15, 84, 16	,  ⊢
	: , :
8	instantiation	121, 89, 17	⊢
	: , : , :
9	instantiation	18, 66, 19, 73, 68, 104	,  ⊢
	: , : , :
10	instantiation	49, 20, 21	,  ⊢
	: , : , :
11	instantiation	49, 22, 23	,  ⊢
	: , : , :
12	theorem		⊢
	proveit.physics.quantum.QPE._modabs_in_full_domain_simp
13	instantiation	24, 97, 115, 85, 25	,  ⊢
	: , : , :
14	instantiation	26, 27	,  ⊢
	:
15	theorem		⊢
	proveit.numbers.addition.add_real_closure_bin
16	instantiation	28, 66	,  ⊢
	:
17	instantiation	121, 96, 29	⊢
	: , : , :
18	theorem		⊢
	proveit.numbers.ordering.less_eq_add_right_strong
19	instantiation	121, 89, 30	⊢
	: , : , :
20	instantiation	57, 113, 123, 58, 41, 59, 52, 75, 43	,  ⊢
	: , : , : , : , : , :
21	instantiation	31, 52, 75, 32	,  ⊢
	: , : , :
22	instantiation	47, 33	⊢
	: , : , :
23	instantiation	49, 34, 35	,  ⊢
	: , : , :
24	theorem		⊢
	proveit.numbers.number_sets.integers.in_interval
25	instantiation	36, 37, 38	,  ⊢
	: , :
26	theorem		⊢
	proveit.numbers.absolute_value.abs_neg_elim
27	instantiation	45, 54	,  ⊢
	: , :
28	theorem		⊢
	proveit.numbers.negation.real_closure
29	instantiation	114, 98, 111	⊢
	: , :
30	instantiation	121, 96, 98	⊢
	: , : , :
31	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_13
32	instantiation	76	⊢
	:
33	instantiation	49, 39, 40	⊢
	: , : , :
34	instantiation	57, 113, 123, 58, 41, 59, 64, 75, 43	,  ⊢
	: , : , : , : , : , :
35	instantiation	42, 75, 43, 44	,  ⊢
	: , : , :
36	theorem		⊢
	proveit.logic.booleans.conjunction.and_if_both
37	instantiation	107, 97, 98, 92	,  ⊢
	: , : , :
38	instantiation	45, 46	,  ⊢
	: , :
39	instantiation	47, 48	⊢
	: , : , :
40	instantiation	49, 50, 51	⊢
	: , : , :
41	instantiation	71	⊢
	: , :
42	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_21
43	instantiation	74, 52	,  ⊢
	:
44	instantiation	76	⊢
	:
45	theorem		⊢
	proveit.numbers.ordering.relax_less
46	instantiation	53, 54, 55	,  ⊢
	: , : , :
47	axiom		⊢
	proveit.logic.equality.substitution
48	instantiation	56, 75, 63	⊢
	: , :
49	axiom		⊢
	proveit.logic.equality.equals_transitivity
50	instantiation	57, 58, 123, 113, 59, 60, 64, 61, 63	⊢
	: , : , : , : , : , :
51	instantiation	62, 63, 64, 65	⊢
	: , : , :
52	instantiation	121, 83, 66	,  ⊢
	: , : , :
53	axiom		⊢
	proveit.numbers.ordering.transitivity_less_less
54	instantiation	67, 68, 69	,  ⊢
	: , : , :
55	instantiation	70, 118	⊢
	:
56	theorem		⊢
	proveit.numbers.negation.distribute_neg_through_binary_sum
57	theorem		⊢
	proveit.numbers.addition.disassociation
58	axiom		⊢
	proveit.numbers.number_sets.natural_numbers.zero_in_nats
59	theorem		⊢
	proveit.core_expr_types.tuples.tuple_len_0_typical_eq
60	instantiation	71	⊢
	: , :
61	instantiation	121, 83, 72	⊢
	: , : , :
62	theorem		⊢
	proveit.numbers.addition.subtraction.add_cancel_triple_32
63	instantiation	121, 83, 73	⊢
	: , : , :
64	instantiation	74, 75	⊢
	:
65	instantiation	76	⊢
	:
66	instantiation	121, 89, 77	,  ⊢
	: , : , :
67	theorem		⊢
	proveit.numbers.ordering.transitivity_less_eq_less
68	instantiation	78, 97, 98, 92	,  ⊢
	: , : , :
69	instantiation	79, 80	⊢
	:
70	theorem		⊢
	proveit.numbers.number_sets.natural_numbers.natural_pos_is_pos
71	theorem		⊢
	proveit.numbers.numerals.decimals.tuple_len_2_typical_eq
72	instantiation	121, 89, 81	⊢
	: , : , :
73	instantiation	121, 89, 82	⊢
	: , : , :
74	theorem		⊢
	proveit.numbers.negation.complex_closure
75	instantiation	121, 83, 84	⊢
	: , : , :
76	axiom		⊢
	proveit.logic.equality.equals_reflexivity
77	instantiation	121, 96, 85	,  ⊢
	: , : , :
78	theorem		⊢
	proveit.numbers.number_sets.integers.interval_upper_bound
79	theorem		⊢
	proveit.numbers.number_sets.integers.negative_if_in_neg_int
80	instantiation	86, 87	⊢
	:
81	instantiation	121, 96, 88	⊢
	: , : , :
82	instantiation	121, 96, 111	⊢
	: , : , :
83	theorem		⊢
	proveit.numbers.number_sets.complex_numbers.real_within_complex
84	instantiation	121, 89, 90	⊢
	: , : , :
85	instantiation	121, 91, 92	,  ⊢
	: , : , :
86	theorem		⊢
	proveit.numbers.negation.int_neg_closure
87	instantiation	93, 94, 95	⊢
	: , :
88	instantiation	119, 111	⊢
	:
89	theorem		⊢
	proveit.numbers.number_sets.real_numbers.rational_within_real
90	instantiation	121, 96, 106	⊢
	: , : , :
91	instantiation	110, 97, 98	⊢
	: , :
92	assumption		⊢
93	theorem		⊢
	proveit.numbers.addition.add_nat_pos_closure_bin
94	instantiation	99, 106, 100	⊢
	:
95	theorem		⊢
	proveit.numbers.numerals.decimals.posnat1
96	theorem		⊢
	proveit.numbers.number_sets.rational_numbers.int_within_rational
97	instantiation	114, 101, 111	⊢
	: , :
98	instantiation	119, 102	⊢
	:
99	theorem		⊢
	proveit.numbers.number_sets.integers.pos_int_is_natural_pos
100	instantiation	103, 104, 105	⊢
	: , : , :
101	instantiation	119, 115	⊢
	:
102	instantiation	114, 106, 111	⊢
	: , :
103	theorem		⊢
	proveit.numbers.ordering.transitivity_less_less_eq
104	theorem		⊢
	proveit.numbers.numerals.decimals.less_0_1
105	instantiation	107, 111, 112, 109	⊢
	: , : , :
106	instantiation	121, 108, 109	⊢
	: , : , :
107	theorem		⊢
	proveit.numbers.number_sets.integers.interval_lower_bound
108	instantiation	110, 111, 112	⊢
	: , :
109	assumption		⊢
110	theorem		⊢
	proveit.numbers.number_sets.integers.int_interval_within_int
111	instantiation	121, 122, 113	⊢
	: , : , :
112	instantiation	114, 115, 116	⊢
	: , :
113	theorem		⊢
	proveit.numbers.numerals.decimals.nat1
114	theorem		⊢
	proveit.numbers.addition.add_int_closure_bin
115	instantiation	121, 117, 118	⊢
	: , : , :
116	instantiation	119, 120	⊢
	:
117	theorem		⊢
	proveit.numbers.number_sets.integers.nat_pos_within_int
118	theorem		⊢
	proveit.physics.quantum.QPE._two_pow_t_minus_one_is_nat_pos
119	theorem		⊢
	proveit.numbers.negation.int_closure
120	instantiation	121, 122, 123	⊢
	: , : , :
121	theorem		⊢
	proveit.logic.sets.inclusion.superset_membership_from_proper_subset
122	theorem		⊢
	proveit.numbers.number_sets.integers.nat_within_int
123	theorem		⊢
	proveit.numbers.numerals.decimals.nat2
*equality replacement requirements